⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠁⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⣶⢦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢀⢸⡏⠀⠀⢀⣀⣀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡏⠀⠀⣠⣴⣦⡀⠸⣿⡷⠶⠾⠻⠛⠛⠃⠀⠀⡿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢽⡇⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠰⣤⣤⠞⠀⠀⠀⠀⢀⢤⢤⠤⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⢀⡴⢶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢵⣁⡧⠃⠀⠀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⢯⣊⡧⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀
⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀
⠀⢀⣠⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠶⣄⠀⠀⠀
⠀⣾⡏⠀⠸⡄⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀
⠰⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⡟⠀
⠀⠈⣿⡆⠀⠀⠀⠀⠘⢆⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡼⠀⠀
⠀⠀⠈⠻⣦⣀⠀⢀⠀⠈⣇⡄⠀⠀⠿⡆⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠈⣶⡾⠟⠀⠀⠀
⠀⠀⠀⠀⠈⢛⣻⡿⠀⠀⠈⣷⡀⠀⠀⢻⡦⠤⠤⠤⠤⠄⡇⠀⠀⠀⢸⡇⠀⠀⣾⣅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣯⣦⣤⣤⣴⣼⣇⠀⠀⠀⣷⡀⠀⠀⠀⣸⡏⠀⢠⠀⢸⣷⣤⣤⣾⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢹⣆⣷⣴⣾⡇⠀⠀⠀⢸⡇⢀⣼⠼⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠃⠀⠀⠀⠀⠀⠀⠱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠂⢀⣁⡀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡴⠿⠛⠫⠭⡓⢦⡀⠠⠀⠀⠀⠀⠠⠂⢀⡴⠞⣛⠛⠲⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠁⣰⠋⠀⠀⠀⠀⠀⣸⣦⠱⡄⠀⠀⠀⠄⢀⡴⡡⠚⠉⠀⢈⣿⣦⡙⣦⠀⠂⠀⠀⠀
⠀⢀⠁⣸⠁⠀⠀⠀⠀⠀⣸⣿⣿⣧⠳⠶⠶⠶⠦⢎⡞⠁⠀⠀⢰⣿⣿⣿⣿⡌⢧⠀⢀⠀⠀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⢂⠐⠄⢂⡞⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠈⡇⠀⡀⠀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⠉⣩⣿⣿⡇⠠⢈⠐⣸⠁⠀⠀⠀⠘⠛⢛⣿⣿⣿⣿⢀⢹⠀⠀⠀
⠀⠄⠸⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⡁⢂⠐⣸⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⢺⡀⢰⠀
⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠐⡀⢂⠐⡘⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠠⢸⠇⢸⠀
⠐⠀⡼⣹⣷⣄⠀⠀⠀⠀⠀⡩⠋⠠⢁⠐⡀⢂⠐⠹⡀⠀⠀⠀⠘⠻⠿⢿⣿⡀⠡⢈⡆⠈⠀
⠁⢰⠇⢻⣟⣿⣳⣶⣶⡶⠋⡑⠌⡐⢀⠂⠌⠠⠈⠴⠛⠢⣀⣀⣀⣀⣴⣾⣟⣿⠄⠂⣟⠀⠀
⠀⢹⡄⢂⠈⠓⠛⠓⡉⠠⠐⡀⠢⠐⠐⠈⠀⠁⡌⠀⠈⠐⠠⠹⠿⣻⡽⣾⡽⠊⠠⢡⠇⢀⠀
⠄⠘⣧⠂⠌⠠⢁⠂⡄⠑⠈⠀⠀⠀⠣⢀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠂⢡⡞⠀⠄⠀
⠀⠀⠙⢷⣌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀
⠀⠀⠠⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢈⠙⠛⠶⠦⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠴⠞⠋⠁⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⣰⣿⢯⣟⣯⣉⣩⡿⣟⣿⣻⣄⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⢄⠎⢀⡾⡿⠯⠿⠚⠛⠛⠿⣽⣻⢾⡽⠀⡙⠳⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠐⣡⠊⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠈⠙⢏⡁⢂⠐⠠⢈⠻⢦⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠂⠅⢀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢄⡟⠑⢮⣐⢀⠂⠄⡙⠷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢠⡿⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡿⠀⠀⠀⠈⠳⣮⡐⢀⠂⠌⢷⡄⠐⠀
⠀⠀⠀⠀⠀⢀⡞⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣼⠁⠐⠀⠀⠈⠂⠈⢳⡄⡈⠐⡈⣿⡀⠁
⠀⠀⠀⠄⢀⡾⢁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⡏⠀⠁⠀⠀⠀⠀⠀⠀⡇⠄⠡⢀⣽⡇⠀
⠀⠀⠌⢠⡿⠁⢂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⠠⢹⡇⢀⠀⠀⠀⠀⠀⠀⣸⠃⠌⡐⢠⡿⠀⠄